Engelhardt and Kumar 209
employment controls are dummy variables for union status, firm-size category, and Census region.
The focal explanatory variable is , which is a function of pension wealth, and
P is defined as the sum of two components. Its basis is self-reported private pension
wealth calculated by Venti and Wise 2001. Because some private pensions are structured so that their benefits are integrated with Social Security benefits, we also
include Social Security wealth, as constructed by Mitchell, Olson, and Steinmeier 1996 and Gustman, Mitchell, Samwick, and Steinmeier 1999, in our measure of
, so that hereafter “self-reported pension wealth” refers to the sum of public and P
private pension wealth. is constructed to take into account the time the household
P has had since the introduction of each pension plan to adjust the lifetime consump-
tion stream using Gale’s Q Gale 1998. This is detailed in the appendix as well. Overall, the analysis sample consists of mostly white, married individuals in their
mid-50s, with some college education and relatively few children at home. Only 57 percent of the sample was employed in a current pension-covered job in 1992.
B. OLS Estimates
In Figure 1, we collapse the analysis sample into age education
race marital
⳯ ⳯
⳯ status cells and plot nonpension wealth versus pension wealth, illustrating the basic
noninstrumented relationship. Contrary to theory, the relationship is strongly posi- tive, suggesting that pension wealth crowds in private saving.
Column 1 of Table 2 shows the OLS crowd-out estimate, , in 1, where
is ˆ
ˆ 
the estimated inverse Mills’ ratio from a Heckman selection correction, with standard
errors in parentheses. We use two exclusion restrictions developed in Engelhardt and Kumar 2007 in the selection equation. The first is derived from IRS Form 5500
data and is the incidence of pension-plan outsourcing by Census region, employ- ment-size category, one-digit SIC code, and union status union plan vs. nonunion
plan cell in 1992, where outsourcing means the plan was administered by an entity other than the employer. The intuition is that the HRS is less likely to obtain an
SPD from the employer if on average in its cell plan administration is outsourced, because more than one contact is needed first the employer, then the plan admin-
istrator to receive the SPD.
5
The second is a dummy variable based on the inter- viewer’s perception of the respondent’s cooperation during the interview that takes
on a value of one for individuals with excellent cooperation, who would be more likely to give the correct name and address of the employer used in the SPD match-
ing process, and zero otherwise. All standard errors and confidence intervals pre- sented in the analysis below were based on 331 bootstrapped replications, which
was the optimal number of replications for this sample based on the method in Andrews and Buchinsky 2000. The selection equation was re-estimated for each
bootstrap sample.
The OLS crowd-out estimate, , in Column 1 is 0.23, with a standard error of
ˆ 0.15, and indicates that an additional dollar of pension wealth raises nonpension net
5. It may well be that plans that are outsourced are better administered and therefore more likely to return the pension provider survey and SPD. However, this is likely more than offset because the SPD request
is significantly less likely to get fulfilled with multiple entities to contact.
210 The
Journal of
Human
Resources
Table 1 Sample Means for Selected Variables, Standard Deviations in Parentheses, Medians in Brackets
1 2
3 4
Analysis Sample Subsamples of the Analysis Sample
Omitted
Variable Not Pension-Covered
Plus Those with Matched SPDs
Not Pension-Covered Pension-Covered with
a Matched SPD Pension-Covered
without a Matched SPD
Nonpension wealth 219,945
253,440 183,044
239,958 494,145
527,916 451,375
562,348 [95,000]
[86,735] [102,000]
[94,724] Pension coverage on the
current job 0.48
1 1
Pension coverage on previous job
0.35 0.37
0.34 0.34
Private pension wealth 75,407
129,480 66,176
161,937 193,598
157,952 [11,412]
[65,921] [9,813]
Social security wealth 123,417
119,206 128,055
123,269 62,141
61,791 62,219
61,857 [122,667]
[117,829] [133,114]
[123,654]
Engelhardt
and Kumar
211 Head’s Age
56.2 56.5
55.8 56.1
4.2 4.4
4.0 4.2
[56.0] [56.0]
[55.0] [56.0]
White 0.81
0.80 0.82
0.82 Female
0.21 0.22
0.21 0.21
Married 0.69
0.68 0.70
0.70 Widowed
0.07 0.08
0.07 0.07
Divorced 0.19
0.20 0.18
0.18 Head high school
0.34 0.34
0.34 0.34
Head some college 0.19
0.18 0.20
0.18 Head college graduate
0.23 0.18
0.29 0.21
Any resident children 0.44
0.43 0.45
0.45 Number of resident children
0.67 0.65
0.70 0.69
0.94 0.94
0.94 0.96
[0] [0]
[0] [0]
Present value of lifetime earnings
464,794 338,117
604,353 496,927
505,762 432,808
542,448 560,359
[332,370] [209,423]
[476,700] [343,187]
Sample size 2,728
1,298 1,430
2,879
Notes: Authors’ calculations from the HRS data. Columns 2 and 3 show descriptive statistics for the two subsamples of the analysis sample. Column 4 shows statistics for those who were omitted from the analysis sample because of the failure of the HRS to match an SPD. Private pension wealth on the current job, social security
wealth, and the present value of lifetime earnings are all Q-adjusted, based on Gale 1998 as described in the appendix. Column 1 shows descriptive statistics for the analysis sample.
212 The Journal of Human Resources
Figure 1 Nonpension Wealth and Pension Wealth
Note: This figure shows a scatter plot of cell mean nonpension wealth versus pension wealth, for cells defined by age, education, race, and marital status. It depicts the basic noninstrumented crowd-out rela-
tionship.
worth by 23 cents. Taken at face value, this suggests that pensions crowd in house- hold saving.
6
The p-value for the test of the null hypothesis that there is no selection is 0.01. However, Column 2 of the table shows the OLS estimate without selection correc-
tion. The crowd-out estimate is 0.20, very similar to the selection-corrected estimate in Column 1. This suggests that while correction for potential selection may be
important from a statistical standpoint, it has little economic impact on the estimates. This turns out to be the case for the IV estimates as well.
C. Construction of the Instrument
